z2∙ z32+z22∙ z3−2Q2g∙W2=0Total HeadIn situations where pressure is expressed as a height it is called head. The prime example of this is the static head is the static pressure divided by the density times gravity. The lab manual gives the total head equation as:Htot=Pρ∙ g+12∙v2g+zChange in Total Head Across the Hydraulic JumpFor this experiment, the change in total head across the hydraulic jump can calculated by the change in the total head between point 2 and 3 in the stream. Therefore, the total head difference is:∆ H=H3−H2=(P3ρ∙g+12∙v32g+z3)−(P2ρ∙g+12∙v2T2g+z2)Both P1and P2are Patm, and v2is the theoretical as well as v3 calculated using the continuity equation :Q2=Q3A2∙ v2T=A3∙v3v3=z2∙v2Tz3Therefore, simplify equation  to:∆ H=H3−H2=(12∙(z2∙v2Tz3)2g+z3)−(12∙v2T2g+z2)(22)(23)(24)(25)
Experimental ProcedureThe procedure used was one that was handed out in the Fluid Mechanics 1 Laboratory Manual1. There was no deviation from this procedure and refer to figure 1 below for a higher understanding of the flow to be studied and the control volume of the hydraulic jump.Figure 1: Schematic of the flow to be studied and the control volume of the hydraulic pump.
Results and DiscussionTable 3: Summary of ResultsResultsFlow 1Flow 2Error Flow 1Error Flow 2V1 Theoretical0.789977630.84719888135.60%46.04%V1 Measured0.5087401770.45715374V2 Theoretical6.8464727897.85584416935.60%46.04%V2 Measured4.4090815374.239061951V31.6215330292.009634555Q0.2152871840.252982213z3 Theoretical0.5648758860.59314145429.93%24.48%z3 Measured0.3958333330.447916667change in H theory0.2476241140.46935854668.27%28.72%change in Hmeasure0.4166666670.604166667Total Head 134.7475456634.99677133Total Head 234.3268808234.32486412Total Head 334.3677185734.44170253When applying Bernoulli’s equation across the sluice gate we find that the velocity is 6.8465 ft/s for the first flow test. For the second flow test the velocity was found to be 7.8558 ft/s. This makes sense because the flow for test two was higher than for test one. Using the flow rate equation the velocities for flow one and flow two are respectively, 4.4091 ft/s and 4.2391 ft/sat point two. These values do not make sense because the flow should have been faster in the second case. This would be caused by incorrect reading of the pitot tube or the tube not being placed parallel with the stream. The velocity upstream of the gate was found using the continuity equation using the velocities found at point two. The velocity at point one for flow one was 0.78998 ft/s and was 0.8472 ft/s for flow two using the theoretical velocities. Using the measuredvelocities at point two we find the velocities at point one are 0.5087 ft/s for flow one and 0.4572 ft/s for flow two. These values do not make sense for the same reason that the measured velocities at point two do not make sense. v1 and v2 have a significant error of 35.6% which couldhave come from friction along the channel and from the transfer at the sluice gate. This could